Solve dy=cosx/3

$$d y = \cos x / 3$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{\cos(x)}{3y}\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3dy=\cos(x)$$

The equation is in standard form.

$$3yd=\cos(x)$$

Divide both sides by 3y.

$$\frac{3yd}{3y}=\frac{\cos(x)}{3y}$$

Dividing by 3y undoes the multiplication by 3y.

$$d=\frac{\cos(x)}{3y}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{\cos(x)}{3y}\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3dy=\cos(x)$$

The equation is in standard form.

$$3yd=\cos(x)$$

Divide both sides by 3y.

$$\frac{3yd}{3y}=\frac{\cos(x)}{3y}$$

Dividing by 3y undoes the multiplication by 3y.

$$d=\frac{\cos(x)}{3y}$$

Solve for x (complex solution)

$$x=-i\ln(\sqrt{9\left(dy\right)^{2}-1}+3dy)+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=-i\ln(-\sqrt{9\left(dy\right)^{2}-1}+3dy)+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$

Solve for x

$$x=ArcCosI(3dy)+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(-1\right)\left(\left(-2\right)\pi n_{2}+ArcCosI(3dy)\right)\text{, }n_{2}\in \mathrm{Z}$$